Steve Bruce's side were unable to find an all-important goal at St. James' Park against Sean Dyche's Clarets and are now without a Premier League win in five games.
Dúbravka was rarely tested during the 90 minutes but although the Slovakian believed there were positives to take for the Magpies, the goalkeeper was ultimately disappointed not to come away with maximum points.
The 31-year-old told nufc.co.uk: "After the game, we feel that we've lost points because although we played better than the last time (against Crystal Place) and created chances, we unfortunately couldn't score a goal.
"There were many positives today though and we have to build on this performance and have to be more dangerous but the players did feel more comfortable today.
"I can understand the fans will be frustrated and we all are as well because we wanted to win, especially with how Burnley played today, just defending and waiting for set pieces.
"We know which way they try to play and they are successful in this kind of way but we feel like we have lost some points.
"I'm glad that we kept a clean sheet but obviously I would have been more happy to win the game. We needed the points but this clean sheet is for all the team as they worked so hard. I don't even know if they had a shot on goal today. They may have created chances from set pieces but that was it.
"Burnley are a tough opponent, especially from set pieces. We have to come with every point in this kind of situation but when you play at home you really want to win, especially against the teams closer to you in the table.
"We created the good moments but we were just missing a goal. That's been our problem in previous games so we are trying to work on it. I thought the players looked good today but like I said, we just needed a goal but hopefully they will come.
"We are not safe yet so hopefully we will collect points but we need to stick with the plan because, as you could see, in some moments we should do it a little bit better but on the other side, we did better than the last game."
There was an early injury concern for Dúbravka, who landed awkwardly after claiming a high ball in the opening stages of the contest but United's number one was fit to continue for the full 90 minutes.
Newcastle quickly turn their attention to the Emirates FA Cup on Tuesday night ahead of their fifth round tie at Championship leaders West Bromwich Albion and Dúbravka believes the club have to grasp their chance of reaching the quarter-finals of the competition for the first time since 2006.
He said: "I went for the cross and straight after the jump, I felt the tightness in the calf or knee. I didn't actually know which it was when I landed on the ground and wasn't sure what was going on but after a few minutes I felt better.
"Hopefully, there is no problems but we will see tomorrow as, in a game, you have a lot of adrenaline during a match so you don't think about it.
"Every game will be difficult and very important for us this season. It is a big opportunity for us in the cup and West Bromwich are in a position where they want to get promoted to the Premier League so we'll see how they will play and what system they will try to play against us."
